^We were shown that Admiral Marcus worked for Section 31, which had an office in London. It's simple to assume he thus lived in England when his daughter was born and raised. Clearly the Prime universe's Marcus family did not live in England. Carol was born after the timeline split, so there's no reason she couldn't have had a different upbringing from day one. After all, this Carol is in Starfleet while Carol Prime is a civilian. So clearly her life is different.

The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.

^We were shown that Admiral Marcus worked for Section 31, which had an office in London. It's simple to assume he thus lived in England when his daughter was born and raised. Clearly the Prime universe's Marcus family did not live in England. Carol was born after the timeline split, so there's no reason she couldn't have had a different upbringing from day one. After all, this Carol is in Starfleet while Carol Prime is a civilian. So clearly her life is different.

The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.

The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.

I just assumed that in the Abramsverse she spent more time around her British mother growing up and in the Prime Universe her father had more of a presence in her life. Hell without the looming threat of a Romulan space octopus that could destroy planets, maybe Alex Marcus Prime wasn't as career driven and eventually retired from Starfleet to focus on a family life?

How do we know she was definitely American in TWOK? (For that matter, how do you know she's British in STID? )

The teenage children of several Brits I know here in the US have lived here so long they've completely lost their British accents.

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Quite true. She could have been British in TWOK just she was rasied say in the USA.

But as someone has already the changed timeline could have any number of consequences. After all Kirk was born in Iowa in the Prime universe on a starhip in the JJverse. No reason as to why someone could be born in the US in the prime universe and the UK in the JJVerse.

The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.

I read somewhere that there was a deleted scene where she says she was raised in London. It's probably still in the novelization, if anyone's read it.

EDIT: He we go!
Still, there are major differences in the two versions of the character – most notably the addition of Eve’s English accent. In fact, Abrams was so concerned that the change would be a sticking point (Marcus had an American accent in the original series), he actually shot an expository scene where the character explains her own backstory – a scene that was eventually cut:

Alice Eve: There was one scene that we shot that didn’t
make it into the film. That was about me explaining why I had an English accent; my mother moved to England when my father stayed in San Francisco to run Starfleet. I think that JJ felt that plot point wasn’t necessary and that you didn’t question it beyond the first moment. I think that made sense and we had a certain license with the split timeline.

The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.

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That is so sad.

Did Americans become dumber between the 1980s and 2010s?

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This has been the case since well before the 1980s. In film certain accents equal "scientist". British English (of a certain type) and German are two of them.

Kirk Prime was "from Iowa," but that doesn't necessarily mean he was born there, just that he mostly lived there. The interpretation that he was born there comes mainly from the city of Riverside's decision to declare themselves Kirk's future birthplace as a draw for tourists. Which the new movie acknowledged by making Kirk a resident of Riverside, but which is not part of the canon.